A Geometrial Approach to the Diophantine Equation x_1^2+x_2^2+...+x_n^2=u^2
Abstract
We find all Diophantine solutions for the equation by refining the geometrical approach from (Ayoub, 1984) to find solutions of the equation We can find all rational points on the unit n-sphere by lines connecting those rational points to the point Such linear parametric equations will always have rational slopes.
Keywords : Diophantine solutions ; Pythagorean triples ; unitsphere
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